Splitting pieces of a mesh into a new object
Select the object.
Enter edit mode (press ↹ Tab)
Press P&gt; Selection to separate the selection into a new object:


From the manual:

Options

Selected
This option separates the selection to a new object.

By Loose Parts
Separates the mesh in its unconnected parts.
By Material
Creates separate mesh objects for each material.

Note that if there are no disconnected parts of the mesh besides the armor, using the By Loose Parts option might be faster.
Also note that you can select linked geometry by:

Pressing L with your mouse over geometry will select all geometry connected to the element below your cursor.

Pressing CtrlL will select all geometry connected to any selected element(s).


To access the option from a menu use Mesh &gt; Separate